Add “Make my homework”, and finish the mobile polish pass

Homework (/homework — entry points in the drawer and on the create screen)

- Assignment intake reuses the study pipeline: pasted text, photos
  (camera/picker, compressed in the browser) and documents (PDF/DOCX/PPTX/
  ODT/text) through lib/image + lib/documents, the same vision step and the
  same language guard. Raw files never leave the device — only text and JPEG
  data URLs reach the server.
- Two large choice cards: “Just make it” returns the finished homework
  (answer only, plain text, copy + make it again); “Explain how to make this
  homework” builds an interactive guide.
- The guide is one step per screen in the study-feed snap layout:
  explanation, three progressive hints (nudge -> hint -> the answer) and an
  optional checkpoint rendered by the existing activity components (graded
  through /api/grade). The last screen assembles the solution from the step
  answers, with a copy button. Checkpoints carry xp 0 so the guide stays free
  of XP/streak chrome.
- Results live in freezmo.homework.v1 with a small history (open/delete);
  “Make it again” re-runs from the stored assignment text (the vision
  transcription when photos were used) — no original files are stored.
- The answer and the guide are written in the assignment's language, never
  translated into the UI language.

Server

- POST /api/homework: NDJSON stage events like /api/generate, the same
  http-guard, auth checked before parsing, and its own RATE_LIMIT_HOMEWORK
  (documented in .env.example + the README table).
- New prompts in lib/prompts.ts and zod schemas in lib/schemas.ts with the
  same single repair retry; TEXT_MODEL for content, VISION_MODEL only for
  photos. New shared client pieces: useNotesIntake, lib/homework store,
  lib/clipboard, and a shared NDJSON reader in lib/client-api.

Also finishing the mobile polish pass from the previous request

- Phone ice scene: the top-left orb moved behind the glass header (it sat
  behind the page heading/subtitle). The settings sheet's scroll cue is now a
  bare chevron inside a content fade (mask) instead of a chip over the status
  banner, and the API key card's note/disclosure/actions are tightened.
- theme-color now follows the in-app theme (SSR metas still fall back to the
  OS preference); apple-mobile-web-app-status-bar-style stays “default”
  because iOS fixes the status-bar text colour at launch.

Verified: 78/78 homework checks (text/photo/PDF, both modes, EN+CS, dark+light,
360/390px, copy, history persistence, storage privacy, API language, axe), plus
the existing suites re-run (mobile 47/47, pixel contrast 0 below AA, i18n 27/27,
desktop regression 72/72). Lint + build clean; service worker freezmo-v6.

components/homework/CopyButton.tsx

@@ -0,0 +1,33 @@
+"use client";
+
+import { useState } from "react";
+
+import { Button } from "@/components/ui";
+import { copyText } from "@/lib/clipboard";
+import { useI18n } from "@/lib/i18n";
+import { cn } from "@/lib/utils";
+
+/** Copy-to-clipboard with a short “Copied!” state and a manual fallback note. */
+export function CopyButton({ text, className }: { text: string; className?: string }) {
+  const { t } = useI18n();
+  const [state, setState] = useState<"idle" | "copied" | "failed">("idle");
+
+  const copy = async () => {
+    const ok = await copyText(text);
+    setState(ok ? "copied" : "failed");
+    window.setTimeout(() => setState("idle"), 2200);
+  };
+
+  return (
+    <span className={cn("inline-flex flex-col items-start gap-1", className)}>
+      <Button className="touch-target" onClick={() => void copy()}>
+        {state === "copied" ? t("homework.result.copied") : t("homework.result.copy")}
+      </Button>
+      {state === "failed" ? (
+        <span role="status" className="text-[12px] text-rose-700 dark:text-rose-300">
+          {t("homework.result.copyFailed")}
+        </span>
+      ) : null}
+    </span>
+  );
+}